The correct statements are: 3-SAT is polynomially reducible to the INDEPENDENT SET language. 3-SAT is polynomially reducible to the VERTEX-COVER language. 3-SAT is polynomially reducible to the EDGE-COVER language. 3-SAT is polynomially reducible to the TSP-DECIDE language.

Can you help me solve this exercise? Please note that the greedy approach described in the advice paragraph does not work.

Answer the given question with a proper explanation and step-by-step solution.  Answer yes or no and Prove or explain precisely why please1. If you can solve TSP in linear time, you can solve the Hamiltonian path problemin linear time.2. If Graph Isomorphism belongs to NPC then P = NP3. The question if a program stops on an input x within n^3 steps or less belongs toNPC.4. The question does a program stops on an input x (namely there is no infiniteloop) belongs to NPC.

write both java and c program for Graph incorporating BFS and DFS algorithms (using recursion).

Show that the vertices reached in each invocation of the recursive method from the constructor are in a strong component in a DFS of a digraph G where marked vertices are taken into account in reverse postorder provided by a DFS of the digraph's reverse GR (Kosaraju's algorithm)

Is this statement about the chromatic number true? Please give some prove and brief explaination: If A and B are graphs on the same vertex-set, then χ(A ∪ B) ⩽ χ(A) + χ(B).

Finding whether an undirected graph is linked or not in C using Wride code?

Write a function that returns true (1) if there is an edge between two vertices u and v in an adjacency-listed directed graph.